dgnd {cmgnd} | R Documentation |
The Generalized Normal Distribution (GND)
Description
Density function for the GND with location parameter mu
,
scale parameter sigma
and shape parameter nu
.
Usage
dgnd(x, mu = 0, sigma = 1, nu = 2)
Arguments
x |
A numeric vector of observations. |
mu |
A numeric value indicating the location parameter |
sigma |
A numeric value indicating the scale parameter |
nu |
A numeric value indicating the shape parameter |
Details
If mu
, sigma
and nu
are not specified
they assume the default values of 0, 1 and 2, respectively.
The GND distribution has density
f_{GND}(x|\mu,\sigma,\nu)=\frac{\nu}{2\sigma\Gamma(1\mathbin{/}\nu)}\exp\Biggr\{-\Biggr|\frac{x-\mu}{\sigma}\Biggr|^\nu\Biggr\}.
The shape parameter \nu
controls both the peakedness and tail weights.
If \nu=1
the GND reduces to the Laplace distribution and if \nu=2
it coincides with the normal distribution. It is noticed that 1<\nu<2
yields an intermediate distribution between the normal and the Laplace distribution.
As limit cases, for \nu\rightarrow\infty
the distribution tends to a uniform
distribution, while for \nu\rightarrow0
it will be impulsive.
Value
dgnd
returns the density.
References
Nadarajah, S. (2005). A generalized normal distribution.
Journal of Applied Statistics, 32(7):685–694
.